This project seeks to estimate sport fish harvest and releases of rockfish in Alaska waters by improving on the Howard et al. (2020) methods and expand the time series back to 1977 when the statewide harvest survey (SWHS) was first implemented. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and replaces the Howard decision tree approach to low sample sizes with a hierarchical model. The methods and results for generating harvest estimates are generally consistent between the Bayesian model and the Howard methods. Harvest estimates are consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data.

The Bayesian methods depart from the Howard method in how releases are estimated. The Howard methods assume that the species composition of the harvests are equal to the species composition of released fish, which is clearly contraindicated in the logbook data. For instance, logbook data demonstrates that yelloweye have been retained at high levels up until restrictions were enacted in recent years, whereas pelagic rockfish were released in significant numbers in the past with retention increasing in recent years as they have become more prized by anglers. Recent prohibition on retaining yelloweye in Southeast Alaska highlights the shortcomings of the original Howard assumptions as the species composition of the harvest would indicate that no yelloweye were caught and released during the closure.

The Howard method for estimating releases for private anglers also relied on an expansion of the logbook release estimates based on the ratio of private:guided releases of all rockfish in the SWHS. In addition to the faulty assumptions about species composition, this method ignores potential bias in SWHS estimates of harvests and releases or at least assumes that the bias in release and harvests are the same. As demonstrated in Figure 1, the bias in those two quantities appears to be quite different based on the logbook data. The Bayesian model thus attempts to estimate release probabilities based on the logbook data coupled with bias corrected estimates from the SWHS.

Lastly, the Howard methods were only used on data beginning in 1999 with the advent of the logbook program and estimates of harvests and releases prior to that have been based on linear ramps from 1999 back to the perceived start of the fishery. The Bayesian methods allow us to expand the time series back to 1977 when the SWHS was implemented by leveraging regional data trends in species composition and the proportion of caught rockfish harvested by species and/or species complex. Key advantages of the Bayesian approach are highlighted in table 1.

Table 1. Summary of key improvements in reconstructiing sport fish removals of rockfish using the Bayesian model as compared to the Howard et al. (2020) methods.
Issue Howard Bayes
Time series 1999 - present 1977 - present
Bias in SWHS Not explicitly dealt with. Relies on logbook data and ratios of guided/unguided from SWHS data to estimate unguided releases and harvests. Explicitly estimates bias in SWHS harvest and release estimates based on logbook data.
Species composition of releases Assumes that species composition of releases is equal to that of the harvest, which is not evident in the logbook data. Recognizes different release probabilities by species / species assemblage and estimates it from logbook data and bias corrected SWHS data
Sample size limitations Uses sample size threshholds such that when areas fall below those threshholds values are borrowed from nearby areas. Uses a hierarchichacal modelling approach that shares information between areas in the same region. Thus all data is used, even with small sample sizes. This is a more sound method that avoids assumptions and uses all of the data.
Error propogation Error is propogated when variance estimates are available, but there is uncertainty associated with borrowing values from nearby areas, or the assumption of species compositions being identical in harvest and releases, are not dealt with. By breaking the assumption that species composition is equal between harvests and releases, uncertainty in the release estimates is more reflective of the fishery. Furthermore, the hyerarchichal approach more accurately captures uncertainy within and between areas within a region.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are overall harvest estimates from 1977- 1995 and release estimates from 1990-1995 that required some partitioning to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied to the pre-1996 values.

**Figure 1.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.

Figure 1.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units. Note that initial rockfish harvest estimates were not differentiated into species assemblage or species until 1998 when logbooks began differentiating by pelagic and non-pelagic. Logbooks began to collect data on yelloweye beginning in 2006. Port sampling programs to gather data on species composition of harvests began in 1996 in Southcentral and Kodiak and in 2006 in Southeast.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook records are a census of guided harvests and releases.

SWHS Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides have been required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 2.**- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).

Figure 2.- SWHS harvest (left) and release (right) estimates from guided trips (x-axis) versus repoted harvests from charter logbooks (y-axis).


A note on model development

To evaluate the discrepancy in apparent bias in harvest and release data, several models were explored to estimate releases during model development. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treated the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases. This tensions eventually highlighted the different release/retention probabilities between yelloweye and pelagics in the logbook data and prompted the current approach whereby that probability was calculated for the three main species complexes covered in the data: pelagics, yelloweye, and “other”. The methods described here follow the (\(LB_{fit}\)) formulation. Based on model behavior it is unlikely that the (\(LB_{cens}\)) model would work as there would not be enough data to estimate release probabilities. However, it may be worth running the (\(LB_{hyb}\)) approach as a sensitivity test at the very least.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish. In Southeast Alaska, the number of Demersal Shelf Rockfish (DSR, of which yelloweye are one species) and slope rockfish are also recorded.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta0_{(comp)ayu} + \frac{\beta1_{(comp)ayu}}{(1 + exp(\beta2_{(comp)ayu}*(y - \beta3_{(comp)ayu})))} + \beta4_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior. \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernible change in composition over the observed time period. \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was used for hindcasting.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested, \(pH_{(comp)ayu}\), by area, year, user group and species grouping. Because release data from the SWHS is for all rockfish and the release data from logbooks is only subdivided into pelagics, yelloweye and “other” (non-pelagic, non-yelloweye), we only estimated \(pH_{(comp)ayu}\) for those categories. Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases. For non-yelloweye DSR and Slope rockfish assemblages in Southeast Alaska \(R_{(DSR)ayu}\) and \(R_{(slope)ayu}\) were estimated from \(R_{(other)ayu}\) using the species composition data from the harvest, thus assuming that slope and DSR assemblages were caught and released at the same rates.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta0_{(pH)ayu} + \frac{\beta1_{(pH)ayuc}}{(1 + exp(\beta2_{(pH)ayuc}*(y - \beta3_{(pH)ayuc})))} + \beta4_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990. As with the compositional trends, \(\beta\) parameters were modeled hierarchically by region. When \(\beta\) parameters were inestimable as a result of no discernable change in harvest probability over the observed time period, \(\beta1\) (scaling factor) and \(\beta2\) (slope) were fixed to 0 so that the long term mean value was applied.

Release mortality (i.e., the number of released rockfish expected to die) was calculated assuming fixed mortality rates developed in each of the regions. Deep water release (DWR) devices were mandated for charter fleets in 2013 and rates were derived from CITATION. Southeast applies basic rates estimated in these studies while Southcentral and Kodiak rates were derived by using historical depth-of-release data to adjust the rates based on area and user group.

The total number of mortalities by year, area, user and species/species assemblage in numbers was calculated by summing harvests and release mortality such that

\[\begin{equation} M_{(comp)ayu}~=~ H_{(comp)ayu} + m_{R-(comp)ayu} * R_{(comp)ayu} \end{equation}\]

where \(m_{R-(comp)ayu}\) is the release mortality rate by year, area, user and species (Figure XX).

Total removals in biomass were converted using the average weight of fish from port sampling?. A minimum sample size per year of X fish was used as the cutoff for including in the data set. Weights were modeled hierarchically to estimate weights in years when data was missing. The total biomass of removals by year, area, user and species was thus

\[\begin{equation} B_{(comp)ayu}~=~ \overline{wt}_{(comp)ayu} * M_{(comp)ayu} \end{equation}\]

where \(\overline{wt}_{(comp)ayu}\) is the mean weight by species, area, user and year.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. As such, the release data are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), a second approaches was considered that loosened the assumption that logbook releases were a census. Methods explored to develope \(LB_{hyb}\) and \(LB_{cens}\) models are detailed at the end of this section.

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs was thus a proportion of the pelagic harvests

\[\begin{equation} x_{(black)ayu}~\sim~\textrm{Binomial}(P_{(black)ayu}, N_{ayu}^{pel}) \end{equation}\]

Yelloweye rockfish in Southcentral and Kodiak were modeled similarly as a proportion of the total number of non-pelagics such that

\[\begin{equation} x_{(yellow_{R2})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R2})ayu}, N_{ayu}^{nonpel}) \end{equation}\]

Southeast areas have several other non-pelagic groupings such that DSR and slope rockfish are a proportion of non-pelagics

\[\begin{equation} x_{(DSR)ayu}~\sim~\textrm{Binomial}(P_{(DSR)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

and

\[\begin{equation} x_{(slope)ayu}~\sim~\textrm{Binomial}(P_{(slope)ayu}, N_{ayu}^{nonpel}) \end{equation}\]

with yelloweye in southeast a proportion of the DSR harvest

\[\begin{equation} x_{(yellow_{R1})ayu}~\sim~\textrm{Binomial}(P_{(yellow_{R1})ayu}, N_{ayu}^{DSR}). \end{equation}\].

Kodiak has limited port sampling beyond the main harbors but has a robust hydroacoustic survey that is used to quantify black rockfish abundance across the management area and uses stereocameras to derive species compositions of the hydroacoustic data. This data was used as supplementary data to further inform the model to the proportion of pelagic rockfish that are black in Kodiak areas. Angler landings in Kodiak show a higher proportion of black rockfish relative to the hydroacoustic survey and thus the proportion of black rockfish in the hydroacoustic sample related to the true proportion such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ P_{(black|pelagic)ayu} + ae_{au} \end{equation}\].

where \(ae_{au}\) is the angler effect for each area and user group modeled hierarchically around a mean of 0. Predicted \(P_{(black|pelagic)ayu}^{HA}\) assumed a beta distribution such that

\[\begin{equation} P_{(black|pelagic)ayu}^{HA} ~\sim~ beta(\alpha_{HA},\beta_{HA}) \end{equation}\]

where

\[\begin{equation} \alpha_{HA} ~=~ (P_{(black|pelagic)ayu}^{HA})^2 * \frac{1 - P_{(black|pelagic)ayu}^{HA}}{\frac{var_{P_{HA}}-1}{P_{(black|pelagic)ayu}^{HA}}}, \end{equation}\]

\[\begin{equation} \beta_{HA} ~=~ (\alpha_{HA}) * \frac{1}{P_{(black|pelagic)ayu}^{HA} - 1}, \end{equation}\]

\[\begin{equation} var_{P_{HA}} ~=~ (P_{(black|pelagic)ayu}^{HA} * cvP_{(black|pelagic)ayu}^{HA})^2 \end{equation}\]

where \(cvP_{(black|pelagic)ayu}^{HA}\) is the coefficient of variation for the hydroacoustic proportions

\[\begin{equation} cvP_{(black|pelagic)ayu}^{HA} ~=~ \frac{\sqrt{varP_{(black|pelagic)ayu}^{HA}}}{P_{(black|pelagic)ayu}^{HA}} \end{equation}\]

and the variance is approximated using the XXXX method as

\[\begin{equation} varP_{(black|pelagic)ayu}^{HA} ~=~ (\frac{1}{n_{pel}})^2 * varN_{black} + (\frac{n_{black}}{n_{pel}^2}) * varN_{pel} \end{equation}\]

where \(varN_{black}\) and \(varN_{black}\) are the variance of the estimated number of black and pelagic rockfish in the hydroacoustic survey, respectively (CITATION).

The average weight of rockfish by species, user, area and year was modeled hierarchically at several levels within regions such that

\[\begin{equation} wt_{(comp)ayu} ~\sim~ Normal(wt_{(comp)au},\sigma_{wt_{(comp)au}}) ~\sim~ Normal(wt_{(comp)a},\sigma_{wt_{(comp)a}}) ~\sim~ Normal(wt_{(comp)region},\sigma_{wt_{(comp)region}}) \end{equation}\]

where region refers to Kodiak, Southcentral and Southeast. Mean weights and variance were calculated as XXX.

Alternative likelihoods for release estimates

To loosen the assumption that logbook release data are an effective census of true releases I explored models that treated logbook release estimates as a lower bound on the estimate of true releases. In a hybrid approach yelloweye and non-pelagic releases are regarded as a reliable census (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates (where censoring implies NA values) such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

This model formulation failed such that there was not enough data to inform pelagic releases and the values did not seem valid. A second approach is being explored that fits the censored data using a lognormal distribution centered around the logbook release value, but also with a lower bound equal to the number of recorded releases such that

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), \sigma_{Ray1}^2\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Logbook data is assumed to be a census and as such there is no estimate of uncertainty. As of this writing, several methods are being examined for how to treat \(\sigma_{Ray1}^2\). Models are being run that attempt to allow the model to estimate \(\sigma_{Ray1}^2\) with priors. A simple model applies a uniform prior (0.1,50) to \(\sigma_{Ray1}^2\). A hierarchichal approach based on regions is also being examined whereby \(\sigma_{Ray1}^2\) is lognormally distributed around hyper priors \(\mu_{\sigma_R}\) and \(\sigma_{\sigma_R}\). Initial efforts have applied a uniform prior on \(\mu_{\sigma_R}\) between 1 and 50 and on \(\sigma_{\sigma_R}\) between 0 and 10.

Priors.

Priors range from uninformative to very informative or fixed. Priors for compositional logistic parameters are in Table 2 and proportion harvest logistic parameters are in Table 3. Until I figure out how to make a nice table in Rmarkdown, please refer to the attached spreadsheet and comp and harvp tabs.

Unresolved issues and outstanding questions:

  1. Reliability of unguided release estimates: These estimates have the least information feeding them and rely on the bias-corrected SWHS release estimates of all rockfish and the trends in release probability evident in the logbook data. The \(\beta4\) term that estimates the guided/unguided effect was given a very informative prior that tied the release probability of private anglers tightly to that of the charter fleet. The model is then trying to balance the three species complex estimates (pelagic, yelloweye and other) so that they sum to the total unguided releases estimated from the bias corrected SWHS data. For the most part this seems reasonable and appears to work, but there are certain areas where the estimates are “wonky”:

    1. Total rockfish releases more or less align with the total releases estimated with the Howard methods. Presumably, much of the discrepancy results from the substantial bias in release estimates from the SWHS. Interestingly, the logbook data indicates that the SWHS underestimates harvests but overestimates releases by a significant factor (Figure 23 and 24 below).
    2. In general, release estimates of black rockfish are substantially lower than those calculated using the Howard methods. Presumably, much of this derives from the bias correction of the SWHS release estimates.
    3. Yelloweye release estimates also differ considerably from the Howard estimates, but unlike black rockfish are sometimes lower and sometimes higher. Two areas in particular are a little head scratching. Yelloweye releases in the Kodiak Northeast area in particular are significantly lower than for guided anglers with the same pattern evident in Cook Inlet to a lesser extent. Cook Inlet yelloweye numbers are very small, so this is a sample size issue with little consequence. The cause of the Kodiak northeast estimates is not clear to me at this point, but the model estimates the proportion harvested by unguided anglers to be much lower than that of guided anglers, even with the informative prior on \(\beta4\). This must be a product of the bias corrected SWHS release estimates and how the model is partitioning that estimate into the 3 species complexes, but itis a bit a of head scratcher.

  2. Proportion guided estimates: There is not much data on this proportion prior to 2011 and it is not modeled with any sort of trend as was done for species composition and harvest proportions. With the exception of Cook Inlet and North Gulf Coast areas, there is little, if any, trend apparent in the data and perhaps this approach is the best available given the data available. However, if there are data sources somewhere that could inform this part of the model they could be incorporated.

  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.

  4. Proportion harvest estimates for non-pelagic, non-yelloweye in Kodiak WKMA: I need to adjust the prior on the inflection point, \(\beta3\), so that it is forced to occur after 2006. Right now the model is estimating inflection in two Kodiak areas before that point where there is no data to justify a shift. The current inflection is a result of the hierachichal model.

  5. Proportion pelagic in PWS and CSEO: The parameters for these particular proportions are very slow to converge. For the CSEO, the estimates of the \(\beta\) parameters are similar to the other Southeast areas, but the mixing is poor over the length of the chains. In this case I think they will ultimately converge with a very long model run and the shape of the curve in the model output looks acceptable. For the two PWS areas the model seems to struggle with the disparate proportional data from the logbook and the port sampling. There is some wandering in the chains of the \(\beta0\) and \(\beta1\) terms and spikiness in the \(\beta2\) terms. I’ve been working on constraining the hyperpriors for PWS \(beta2\). Similar to CSEO, it may just entail a very long model run to reach convergence, but the shape of the curves looks reasonable.

Next steps:

Once the model is finalized, harvest and release numbers need to be converted into biomass removals. This is a two step process where release mortality estimates are applied to the release estimates to estimate the number of released rockfish that do not survive. This is based on studies and will reflect the values that the department has been using with the Howard methods. Region 2 (both Southcentral and Kodiak) have release-at-depth estimates from a number of years that they apply across all years and then calculate mortality rates based on those estiates. Southease does not have release-at-depth data and simply applies an assumed rate based on research.

Once release mortality is calculated average weight data is applied to convert numbers to biomass. The plan is to incorporate all of this into the model to propogate uncertainty into the posteriors. However, the model already takes a long time to run and I may explore a simpler approach using the posteriors from the numbers model to speed up processing.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 3.**- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.





**Figure 8.**- DSR rockfish (excluding yelloweye) harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 8.- DSR rockfish (excluding yelloweye) harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 9.**- DSR rockfish releases (including yelloweye) 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 9.- DSR rockfish releases (including yelloweye) 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 11.**- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 11.- Slope rockfish harvests 1996-2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 12.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 12.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Total Biomass Removal Estimates

**Figure 13.**- Black rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 13.- Black rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.



**Figure 14.**- Yellow rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 14.- Yellow rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

**Figure 15.**- Pelagic rockfish estimated total removals in lbs in 1996--2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 15.- Pelagic rockfish estimated total removals in lbs in 1996–2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 16.**- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 16.- Non-yelloweye, demersal shelf rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


**Figure 17.**- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.

Figure 17.- Slope rockfish estimated total removals in lbs in 1996-2023. Total removals are calculated from the harvests, the estimated release mortality and mean fish weights. Error polygons represent 95% confidence intervals.


Model fit

Logbook residuals

**Figure 18.**- Residuals from logbook harvests.

Figure 18.- Residuals from logbook harvests.


SWHS residuals

**Figure 19.**- Residuals from SWHS harvests.

Figure 19.- Residuals from SWHS harvests.



**Figure 20.**- Residual of SWHS releases.

Figure 20.- Residual of SWHS releases.

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 21.**- Mean percent of harvest by charter anglers.

Figure 21.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although the model smooths out the changes and we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 22.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 22.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 23.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 23.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 24.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 24.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 25.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 25.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species. 


## NULL


## NULL

SWHS bias

Figure 23 shows the mean estimate for SWHS bias in harvests and releases. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias. Bias in release estimates is substantial and whereas the SWHS appears to underestimate harvests, it appears to greatly overestimates releases by a factor of 2 or more in most areas as derived from logbook reported releases.

**Figure 28.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 28.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS harvest bias track observations fairly well when he have guided harvest estimates. The estimates of release bias in the SWHS data track observed patterns to an extent, but appear to smooth these more volatile disagreements with the logbook data. Adam postulated in his initial start on this that some of this could be the result of the estimates of the proportion guided. This value was not modelled with a trend and thus applies a constant estimate when hindcasting. Data on these relationships could greatly improve this model.

**Figure 29.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 29.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 25 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 30.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 30.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment. For the most part, P(black|pelagic) is relatively constant across areas, with the exception of Cook Inlet and NSEI in Southeast AK. It may be worth discussing whether the shifts in those areas is a result of improved or changing species identification rather than actual shift in the species composition of the catch.

**Figure 31.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

Figure 31.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023. Kodiak panels include data from a hydroacoustic survey and the proportion of pelagic rockfish that are black in those areas (red) and the adjusted proportions based on obseved harvests for charter (blue) and private (cyan) users.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 32.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 32.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 33.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 33.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 34.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 34.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



P(slope|non-pelagic & non-yellowye) For release estimates

**Figure 35.**- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.

Figure 35.- Annual estimates of the percent of the sport non-pelagic, non-yelloweye releases that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023.



Weight Fits

**Figure 36.**- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 36.- Mean weights of black rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 37.**- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 37.- Mean weights of yelloweye rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 38.**- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 38.- Mean weights of non-black, pelagic rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 39.**- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 39.- Mean weights of non-yelloweye, demersal shelf rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


**Figure 40.**- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.

Figure 40.- Mean weights of slope rockfish used to estimate biomass from harvest and release mortality estimates in numbers of fish.


### Summary of unconverged parameters:

##   [1] "pG"             "H_ayu"          "H_ay"           "Hd_ayu"        
##   [5] "Hd_ay"          "Hp_ayu"         "Hp_ay"          "Tp_ayu"        
##   [9] "Bp_ayu"         "Tp_ay"          "Bp_ay"          "Ho_ayu"        
##  [13] "Ho_ay"          "Hdnye_ayu"      "Hdnye_ay"       "Hb_ayu"        
##  [17] "Hy_ayu"         "Tb_ayu"         "Hs_ayu"         "Hy_ay"         
##  [21] "Bb_ayu"         "Hs_ay"          "Hb_ay"          "Tb_ay"         
##  [25] "Bb_ay"          "re_pelagic"     "logbc_H"        "beta3_pH"      
##  [29] "Tdnye_ayu"      "Bdnye_ayu"      "Tdnye_ay"       "Bs_ayu"        
##  [33] "Ts_ayu"         "Ts_ay"          "Bs_ay"          "Bdnye_ay"      
##  [37] "beta2_pH"       "beta1_pH"       "mu_beta2_pH"    "Ry_ayu"        
##  [41] "Ry_ayu_mort"    "Ry_ay"          "Ry_ay_mort"     "re_pH"         
##  [45] "Ro_ayu"         "Rs_ayu"         "Rs_ayu_mort"    "Rs_ay_mort"    
##  [49] "Ro_ay"          "Rdnye_ayg"      "Rdnye_ayg_mort" "Ro_ayg"        
##  [53] "Rs_ay"          "Rdnye_ay"       "Rdnye_ay_mort"  "Rd_ayg"        
##  [57] "Rs_ayg"         "Rs_ayg_mort"    "beta0_pH"       "Rdnye_ayu"     
##  [61] "Rdnye_ayu_mort" "Rb_ayu"         "Rb_ayu_mort"    "Rp_ayu"        
##  [65] "Rp_ayu_mort"    "Ry_ayg"         "Ry_ayg_mort"    "Rb_ay_mort"    
##  [69] "Rb_ay"          "Rp_ay"          "Rp_ay_mort"     "Rd_ay"         
##  [73] "pH"             "Rp_ayg"         "Rp_ayg_mort"    "Rb_ayg"        
##  [77] "Rb_ayg_mort"    "R_ayg"          "By_ayu"         "Htrend_ay"     
##  [81] "R_ayu"          "Rd_ayu"         "mu_beta1_pH"    "pDSR_YE_ay"    
##  [85] "mu_beta0_pH"    "p_dsr"          "By_ay"          "p_yellow"      
##  [89] "pDSR_YE_ayu"    "Hy_ayg"         "Ty_ayg"         "Ho_ayg"        
##  [93] "tau_beta0_pH"   "Bdnye_ayg"      "Tdnye_ayg"      "R_ay"          
##  [97] "pDSR_YE_ayg"    "p_pelagic"      "By_ayg"         "Ts_ayg"
Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_pelagic 6 1.417303
beta3_yellow 1 1.376362
beta0_pelagic 4 1.369689
beta2_pH 14 1.243289
beta3_pH 7 1.226844
beta1_yellow 2 1.210643
beta1_pH 15 1.200279
beta2_pelagic 4 1.196708
parameter n badRhat_avg
beta3_pelagic 4 1.188544
beta0_pH 8 1.171102
mu_beta0_pH 1 1.154957
beta2_yellow 2 1.154361
tau_beta0_yellow 1 1.148408
beta0_yellow 3 1.145916
tau_beta0_pH 1 1.129735
Table 2. Summary of unconverged major parameters by area
Parameter CI NG PWSI PWSO BSAI SOKO2SAP WKMA afognak eastside northeast CSEO EWYKT NSEI NSEO SSEI SSEO
beta0_pH 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1
beta0_pH 1 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1
beta1_pH 1 0 1 1 2 1 1 0 1 1 1 1 1 1 1 1
beta1_pH 1 0 1 1 1 1 1 0 1 1 1 1 1 1 1 1
beta2_pH 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1
beta2_pH 1 1 0 1 0 1 1 1 1 1 1 1 1 1 1 1
beta3_pH 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 2
beta3_pH 1 0 0 0 0 0 0 0 0 0 1 1 1 1 0 1
Bp_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Bp_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
H_ay 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
H_ayu 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Hb_ay 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Hb_ayu 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Hd_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hd_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Ho_ay 0 0 0 0 2 1 0 0 0 0 0 0 1 0 0 0
Ho_ayg 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0
Ho_ayu 0 0 0 0 2 2 1 0 1 0 0 0 1 0 0 0
Hp_ay 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Hp_ayu 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Hs_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hs_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Htrend_ay 0 0 0 0 0 0 0 0 0 0 0 0 14 0 0 0
Hy_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
Hy_ayg 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0
Hy_ayu 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
logbc_H 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta0_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta1_pH 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
mu_beta2_pH 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0
p_dsr 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0
p_pelagic 0 0 0 1 0 0 0 0 0 0 1 0 0 0 0 1
p_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0
pDSR_YE_ay 0 0 0 0 0 0 0 0 0 0 0 0 1 1 0 0
pDSR_YE_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
pDSR_YE_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0
pG 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
pH 9 0 0 0 0 0 0 0 0 0 1 0 2 8 3 0
R_ay 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0
R_ayg 1 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0
R_ayu 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
Rb_ay 9 0 0 0 0 0 3 0 0 0 0 1 0 12 0 0
Rb_ay_mort 8 0 0 0 0 0 3 0 0 0 0 1 0 12 0 0
Rb_ayg 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0
Rb_ayg_mort 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0
Rb_ayu 9 1 0 1 0 0 0 0 0 1 0 1 1 12 0 0
Rb_ayu_mort 9 1 0 1 0 0 0 0 0 1 0 1 1 12 0 0
Rd_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9
Rd_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 14
Rd_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4
Rdnye_ay 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17
Rdnye_ay_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17
Rdnye_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17
Rdnye_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 17
Rdnye_ayu 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
Rdnye_ayu_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
re_pelagic 0 0 0 1 0 0 0 0 0 0 9 0 0 0 0 33
re_pH 18 0 0 0 0 0 0 13 0 9 20 21 19 21 18 22
Ro_ay 1 0 0 0 18 9 0 0 1 0 0 0 0 0 0 17
Ro_ayg 5 0 0 0 1 0 1 1 0 1 0 0 0 0 0 17
Ro_ayu 0 0 0 0 20 9 1 1 2 0 0 0 0 0 0 11
Rp_ay 9 0 0 0 0 0 3 1 0 0 0 1 0 12 0 0
Rp_ay_mort 9 0 0 0 0 0 3 1 0 0 0 1 0 12 0 0
Rp_ayg 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0
Rp_ayg_mort 0 0 0 0 0 0 3 1 0 0 0 0 0 0 0 0
Rp_ayu 9 1 0 1 0 0 0 0 0 1 0 1 0 12 0 0
Rp_ayu_mort 9 1 0 1 0 0 0 0 0 1 0 1 0 12 0 0
Rs_ay 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 14
Rs_ay_mort 0 0 0 0 0 0 0 0 0 0 1 4 0 0 0 14
Rs_ayg 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
Rs_ayg_mort 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 11
Rs_ayu 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 8
Rs_ayu_mort 0 0 0 0 0 0 0 0 0 0 2 5 0 0 0 8
Ry_ay 0 0 0 0 10 2 0 0 0 0 0 0 0 0 0 0
Ry_ay_mort 0 0 0 0 10 2 0 0 0 0 0 0 0 0 0 0
Ry_ayg 1 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0
Ry_ayg_mort 1 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0
Ry_ayu 0 0 0 0 10 2 0 0 0 0 0 0 0 0 0 0
Ry_ayu_mort 0 0 0 0 10 2 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Tp_ay 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
Tp_ayu 0 0 0 0 1 0 0 0 0 0 0 0 1 0 0 0
beta0_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 0 0 0 1
beta0_yellow 0 0 0 1 0 0 0 0 0 0 0 0 1 1 0 0
beta1_pelagic 0 0 1 1 0 0 0 0 0 0 1 0 1 1 0 1
beta1_yellow 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0
beta2_pelagic 0 0 0 0 0 0 0 0 0 0 1 0 1 1 0 1
beta2_yellow 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1
beta3_pelagic 0 0 0 1 0 0 0 0 0 0 1 0 0 1 0 1
beta3_yellow 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0
tau_beta0_yellow 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.126 0.074 -0.263 -0.130 0.026
mu_bc_H[2] -0.093 0.046 -0.171 -0.098 0.009
mu_bc_H[3] -0.428 0.069 -0.558 -0.429 -0.286
mu_bc_H[4] -0.996 0.189 -1.372 -0.994 -0.625
mu_bc_H[5] 0.871 0.858 -0.181 0.709 3.172
mu_bc_H[6] -2.141 0.318 -2.756 -2.145 -1.502
mu_bc_H[7] -0.460 0.110 -0.678 -0.459 -0.252
mu_bc_H[8] 0.249 0.352 -0.369 0.225 1.046
mu_bc_H[9] -0.292 0.134 -0.547 -0.292 -0.030
mu_bc_H[10] -0.103 0.072 -0.236 -0.106 0.045
mu_bc_H[11] -0.126 0.037 -0.202 -0.126 -0.053
mu_bc_H[12] -0.259 0.107 -0.484 -0.254 -0.059
mu_bc_H[13] -0.128 0.080 -0.285 -0.129 0.031
mu_bc_H[14] -0.309 0.100 -0.515 -0.304 -0.119
mu_bc_H[15] -0.340 0.050 -0.439 -0.340 -0.240
mu_bc_H[16] -0.282 0.371 -0.924 -0.314 0.554
mu_bc_R[1] 1.328 0.144 1.051 1.324 1.613
mu_bc_R[2] 1.457 0.094 1.269 1.459 1.637
mu_bc_R[3] 1.395 0.143 1.100 1.395 1.672
mu_bc_R[4] 0.925 0.205 0.489 0.937 1.302
mu_bc_R[5] 1.212 0.458 0.292 1.207 2.101
mu_bc_R[6] -1.580 0.418 -2.389 -1.581 -0.769
mu_bc_R[7] 0.438 0.207 0.009 0.442 0.817
mu_bc_R[8] 0.548 0.189 0.166 0.554 0.901
mu_bc_R[9] 0.342 0.207 -0.083 0.362 0.702
mu_bc_R[10] 1.313 0.173 0.950 1.322 1.625
mu_bc_R[11] 1.051 0.099 0.856 1.051 1.247
mu_bc_R[12] 0.825 0.202 0.419 0.829 1.212
mu_bc_R[13] 1.034 0.105 0.823 1.035 1.239
mu_bc_R[14] 0.900 0.142 0.607 0.903 1.176
mu_bc_R[15] 0.787 0.111 0.567 0.788 0.999
mu_bc_R[16] 1.090 0.128 0.835 1.091 1.343
tau_pH[1] 4.803 1.072 0.969 5.055 6.011
tau_pH[2] 1.970 0.224 1.559 1.957 2.438
tau_pH[3] 2.128 0.223 1.716 2.117 2.587
beta0_pH[1,1] 0.682 0.403 0.229 0.598 1.987
beta0_pH[2,1] 1.411 0.268 0.994 1.388 2.092
beta0_pH[3,1] 1.462 0.266 0.999 1.451 2.068
beta0_pH[4,1] 1.663 0.330 1.192 1.620 2.779
beta0_pH[5,1] -0.774 0.408 -1.432 -0.813 0.390
beta0_pH[6,1] -0.661 0.496 -1.842 -0.602 0.223
beta0_pH[7,1] -0.375 0.574 -1.914 -0.371 0.695
beta0_pH[8,1] -0.558 0.305 -1.124 -0.568 0.085
beta0_pH[9,1] -0.550 0.353 -1.105 -0.581 0.391
beta0_pH[10,1] 0.379 0.276 -0.106 0.365 1.217
beta0_pH[11,1] -0.018 0.465 -0.474 -0.109 1.821
beta0_pH[12,1] 0.553 0.324 0.121 0.512 1.814
beta0_pH[13,1] 0.085 0.375 -0.295 0.018 1.656
beta0_pH[14,1] -0.238 0.380 -0.662 -0.296 1.440
beta0_pH[15,1] 0.059 0.363 -0.380 -0.003 1.363
beta0_pH[16,1] -0.329 0.557 -1.174 -0.372 1.841
beta0_pH[1,2] 2.837 0.160 2.516 2.840 3.144
beta0_pH[2,2] 2.884 0.138 2.605 2.886 3.150
beta0_pH[3,2] 3.134 0.154 2.858 3.127 3.457
beta0_pH[4,2] 2.951 0.131 2.694 2.950 3.212
beta0_pH[5,2] 4.797 1.391 3.004 4.505 8.296
beta0_pH[6,2] 3.124 0.216 2.705 3.119 3.553
beta0_pH[7,2] 1.840 0.198 1.438 1.845 2.219
beta0_pH[8,2] 2.871 0.180 2.525 2.871 3.236
beta0_pH[9,2] 3.438 0.219 3.003 3.442 3.866
beta0_pH[10,2] 3.688 0.211 3.293 3.686 4.107
beta0_pH[11,2] -4.887 0.308 -5.510 -4.873 -4.308
beta0_pH[12,2] -4.804 0.394 -5.614 -4.799 -4.042
beta0_pH[13,2] -4.602 0.398 -5.334 -4.611 -3.790
beta0_pH[14,2] -5.600 0.461 -6.526 -5.589 -4.753
beta0_pH[15,2] -4.297 0.346 -4.941 -4.302 -3.593
beta0_pH[16,2] -4.883 0.395 -5.674 -4.869 -4.140
beta0_pH[1,3] -0.202 0.805 -2.019 -0.082 1.040
beta0_pH[2,3] 2.195 0.161 1.880 2.195 2.513
beta0_pH[3,3] 2.531 0.148 2.233 2.532 2.820
beta0_pH[4,3] 2.970 0.161 2.659 2.970 3.282
beta0_pH[5,3] 2.134 1.475 0.329 1.818 5.875
beta0_pH[6,3] 0.997 0.505 -0.175 1.018 1.894
beta0_pH[7,3] 0.630 0.172 0.306 0.627 0.978
beta0_pH[8,3] 0.308 0.197 -0.073 0.311 0.700
beta0_pH[9,3] -0.642 0.389 -1.581 -0.605 0.011
beta0_pH[10,3] 0.478 0.393 -0.533 0.526 1.104
beta0_pH[11,3] -0.136 0.337 -0.776 -0.137 0.548
beta0_pH[12,3] -0.854 0.351 -1.604 -0.839 -0.239
beta0_pH[13,3] -0.111 0.322 -0.783 -0.118 0.521
beta0_pH[14,3] -0.257 0.259 -0.740 -0.267 0.267
beta0_pH[15,3] -0.724 0.297 -1.284 -0.724 -0.145
beta0_pH[16,3] -0.395 0.308 -1.005 -0.392 0.217
beta1_pH[1,1] 2.839 0.755 0.020 2.995 3.671
beta1_pH[2,1] 2.083 0.429 1.023 2.113 2.722
beta1_pH[3,1] 1.920 0.451 0.860 1.936 2.754
beta1_pH[4,1] 2.233 0.555 0.014 2.309 2.993
beta1_pH[5,1] 2.210 0.462 1.319 2.229 2.962
beta1_pH[6,1] 3.676 1.268 1.328 3.488 6.487
beta1_pH[7,1] 2.385 1.109 0.359 2.324 5.443
beta1_pH[8,1] 3.619 0.990 1.304 3.570 5.488
beta1_pH[9,1] 2.210 0.479 0.908 2.240 2.988
beta1_pH[10,1] 2.158 0.446 0.830 2.196 2.823
beta1_pH[11,1] 3.159 0.660 0.001 3.285 3.794
beta1_pH[12,1] 2.452 0.484 0.001 2.522 2.969
beta1_pH[13,1] 2.840 0.578 0.002 2.935 3.381
beta1_pH[14,1] 3.298 0.618 0.001 3.399 3.865
beta1_pH[15,1] 2.416 0.521 0.001 2.509 2.962
beta1_pH[16,1] 3.918 0.956 0.001 3.959 5.447
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.000 0.002 0.000 0.000 0.001
beta1_pH[4,2] 0.000 0.001 0.000 0.000 0.000
beta1_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.716 0.336 6.087 6.704 7.387
beta1_pH[12,2] 6.461 0.453 5.578 6.447 7.408
beta1_pH[13,2] 6.980 0.432 6.106 6.986 7.819
beta1_pH[14,2] 7.240 0.484 6.337 7.226 8.228
beta1_pH[15,2] 6.771 0.383 6.009 6.780 7.496
beta1_pH[16,2] 7.479 0.431 6.653 7.473 8.325
beta1_pH[1,3] 4.746 1.709 2.123 4.492 8.222
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 4.807 13.121 0.866 2.829 14.132
beta1_pH[6,3] 3.170 3.875 0.423 2.651 9.451
beta1_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,3] 2.747 0.347 2.063 2.740 3.442
beta1_pH[9,3] 2.766 0.457 1.993 2.723 3.887
beta1_pH[10,3] 2.899 0.469 2.134 2.850 3.988
beta1_pH[11,3] 2.717 0.403 1.949 2.714 3.508
beta1_pH[12,3] 4.098 0.434 3.275 4.088 5.002
beta1_pH[13,3] 1.684 0.347 0.998 1.688 2.360
beta1_pH[14,3] 2.503 0.337 1.846 2.509 3.139
beta1_pH[15,3] 2.010 0.325 1.396 2.023 2.621
beta1_pH[16,3] 1.797 0.354 1.072 1.805 2.470
beta2_pH[1,1] 0.302 0.774 -2.503 0.461 0.861
beta2_pH[2,1] 0.595 0.825 0.221 0.523 1.774
beta2_pH[3,1] 0.703 1.061 0.172 0.552 3.015
beta2_pH[4,1] 0.503 0.836 -0.134 0.443 1.951
beta2_pH[5,1] 1.478 1.179 0.234 1.293 4.477
beta2_pH[6,1] 0.237 0.758 0.083 0.177 0.658
beta2_pH[7,1] 0.105 0.816 0.000 0.000 0.509
beta2_pH[8,1] 0.328 0.762 0.141 0.246 0.917
beta2_pH[9,1] 0.478 0.746 0.167 0.394 1.281
beta2_pH[10,1] 0.657 0.649 0.249 0.563 1.616
beta2_pH[11,1] 0.699 1.073 0.356 0.732 1.577
beta2_pH[12,1] 1.250 1.203 0.594 1.233 2.824
beta2_pH[13,1] 0.670 1.107 0.363 0.711 1.446
beta2_pH[14,1] 0.783 1.055 0.456 0.800 1.509
beta2_pH[15,1] 0.724 1.114 -0.152 0.743 1.800
beta2_pH[16,1] 0.264 0.914 -2.003 0.325 0.960
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.026 1.901 -6.975 -1.509 -0.022
beta2_pH[4,2] -1.971 1.787 -6.572 -1.480 -0.024
beta2_pH[5,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[6,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[9,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -9.224 4.402 -20.587 -8.083 -3.927
beta2_pH[12,2] -7.872 5.048 -20.525 -6.883 -1.045
beta2_pH[13,2] -7.687 5.043 -19.943 -6.592 -1.709
beta2_pH[14,2] -8.322 4.669 -20.586 -7.224 -2.595
beta2_pH[15,2] -9.061 4.461 -20.089 -7.982 -3.552
beta2_pH[16,2] -9.319 4.422 -20.210 -8.279 -3.733
beta2_pH[1,3] 0.256 0.415 0.100 0.179 0.749
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 9.125 6.599 -0.332 8.040 23.691
beta2_pH[6,3] 9.231 6.381 0.163 8.229 24.217
beta2_pH[7,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,3] 10.161 5.873 1.899 9.073 24.624
beta2_pH[9,3] 9.115 6.431 0.493 8.058 23.935
beta2_pH[10,3] 8.673 6.679 0.479 7.590 23.737
beta2_pH[11,3] -2.344 2.195 -8.616 -1.688 -0.563
beta2_pH[12,3] -2.500 2.086 -8.731 -1.867 -0.959
beta2_pH[13,3] -2.968 2.436 -9.586 -2.192 -0.694
beta2_pH[14,3] -2.913 2.382 -9.934 -2.145 -0.854
beta2_pH[15,3] -3.080 2.448 -10.219 -2.250 -1.043
beta2_pH[16,3] -2.921 2.695 -10.008 -2.186 0.802
beta3_pH[1,1] 35.072 3.692 19.853 35.854 37.666
beta3_pH[2,1] 33.461 1.716 31.038 33.418 36.481
beta3_pH[3,1] 33.631 1.707 31.092 33.629 36.044
beta3_pH[4,1] 33.769 2.219 29.569 33.831 37.272
beta3_pH[5,1] 27.902 1.876 26.305 27.487 32.864
beta3_pH[6,1] 38.112 3.594 31.261 37.933 45.076
beta3_pH[7,1] 31.045 8.116 18.607 30.645 45.195
beta3_pH[8,1] 39.300 2.818 34.212 39.505 43.473
beta3_pH[9,1] 30.839 1.953 28.015 30.729 34.735
beta3_pH[10,1] 32.913 1.487 30.855 32.894 35.314
beta3_pH[11,1] 30.558 1.490 29.399 30.329 33.939
beta3_pH[12,1] 30.284 0.905 29.314 30.186 31.944
beta3_pH[13,1] 33.344 1.374 31.999 33.159 36.515
beta3_pH[14,1] 32.140 1.071 31.103 32.031 33.277
beta3_pH[15,1] 31.355 1.065 30.000 31.233 33.112
beta3_pH[16,1] 32.543 1.987 30.568 32.118 39.277
beta3_pH[1,2] 30.268 8.048 18.527 29.279 45.104
beta3_pH[2,2] 30.154 8.007 18.467 29.319 44.890
beta3_pH[3,2] 30.011 8.025 18.416 29.158 44.934
beta3_pH[4,2] 29.781 8.014 18.403 28.821 44.978
beta3_pH[5,2] 29.878 7.981 18.458 28.894 44.919
beta3_pH[6,2] 29.917 8.037 18.432 28.830 45.028
beta3_pH[7,2] 30.108 7.988 18.425 28.921 44.877
beta3_pH[8,2] 29.951 8.000 18.456 28.890 44.808
beta3_pH[9,2] 29.838 7.929 18.432 29.068 44.804
beta3_pH[10,2] 30.046 7.909 18.516 29.173 44.696
beta3_pH[11,2] 43.411 0.177 43.125 43.391 43.779
beta3_pH[12,2] 43.191 0.192 42.912 43.145 43.673
beta3_pH[13,2] 43.864 0.149 43.479 43.907 44.045
beta3_pH[14,2] 43.295 0.197 43.048 43.244 43.799
beta3_pH[15,2] 43.413 0.193 43.108 43.392 43.808
beta3_pH[16,2] 43.491 0.187 43.159 43.489 43.841
beta3_pH[1,3] 38.941 3.349 32.324 38.853 45.388
beta3_pH[2,3] 30.307 7.849 18.423 29.590 44.862
beta3_pH[3,3] 29.842 7.994 18.438 28.827 44.764
beta3_pH[4,3] 30.313 7.878 18.485 29.631 44.991
beta3_pH[5,3] 36.717 3.872 31.216 36.230 44.968
beta3_pH[6,3] 40.510 3.458 31.672 40.889 45.526
beta3_pH[7,3] 37.994 4.296 31.368 37.697 45.555
beta3_pH[8,3] 41.487 0.250 41.059 41.491 41.919
beta3_pH[9,3] 33.481 0.574 31.692 33.567 34.326
beta3_pH[10,3] 35.844 0.802 33.472 36.024 36.866
beta3_pH[11,3] 41.808 0.814 40.226 41.801 43.374
beta3_pH[12,3] 41.724 0.396 40.950 41.734 42.508
beta3_pH[13,3] 42.762 0.943 41.012 42.763 44.902
beta3_pH[14,3] 41.090 0.597 39.851 41.108 42.209
beta3_pH[15,3] 42.629 0.645 41.289 42.669 43.751
beta3_pH[16,3] 42.404 2.750 29.891 43.039 44.139
beta0_pelagic[1] 2.225 0.129 1.968 2.224 2.480
beta0_pelagic[2] 1.516 0.126 1.266 1.518 1.761
beta0_pelagic[3] -0.237 0.551 -1.591 -0.115 0.522
beta0_pelagic[4] -0.220 0.644 -1.531 -0.120 0.803
beta0_pelagic[5] 1.194 0.254 0.667 1.197 1.680
beta0_pelagic[6] 1.453 0.275 0.863 1.473 1.957
beta0_pelagic[7] 1.609 0.212 1.229 1.594 2.092
beta0_pelagic[8] 1.763 0.208 1.366 1.752 2.199
beta0_pelagic[9] 2.467 0.320 1.829 2.476 3.069
beta0_pelagic[10] 2.493 0.212 2.020 2.504 2.895
beta0_pelagic[11] -0.354 0.510 -1.233 -0.396 0.584
beta0_pelagic[12] 1.685 0.147 1.392 1.687 1.969
beta0_pelagic[13] 0.262 0.209 -0.178 0.271 0.652
beta0_pelagic[14] -0.142 0.307 -0.892 -0.113 0.364
beta0_pelagic[15] -0.241 0.138 -0.504 -0.246 0.034
beta0_pelagic[16] 0.289 0.261 -0.379 0.350 0.658
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.677 0.856 0.533 1.545 4.008
beta1_pelagic[4] 1.569 0.754 0.414 1.452 3.181
beta1_pelagic[5] -0.071 0.305 -0.664 -0.070 0.518
beta1_pelagic[6] -0.080 0.457 -0.876 -0.121 0.760
beta1_pelagic[7] -0.032 0.292 -0.605 -0.036 0.543
beta1_pelagic[8] -0.008 0.284 -0.562 -0.015 0.541
beta1_pelagic[9] 0.223 0.493 -0.796 0.341 0.974
beta1_pelagic[10] 0.079 0.275 -0.456 0.074 0.635
beta1_pelagic[11] 4.657 1.222 2.549 4.576 7.027
beta1_pelagic[12] 2.803 0.316 2.198 2.797 3.457
beta1_pelagic[13] 3.218 0.849 1.996 3.025 5.124
beta1_pelagic[14] 4.498 1.085 2.867 4.374 6.915
beta1_pelagic[15] 2.891 0.259 2.346 2.899 3.388
beta1_pelagic[16] 3.669 1.069 2.686 3.299 7.058
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 0.739 2.332 0.045 0.186 6.914
beta2_pelagic[4] 1.353 3.179 0.045 0.370 12.158
beta2_pelagic[5] -0.003 0.671 -1.403 -0.011 1.387
beta2_pelagic[6] -0.057 0.721 -1.430 -0.106 1.523
beta2_pelagic[7] -0.001 0.629 -1.273 -0.007 1.371
beta2_pelagic[8] 0.022 0.647 -1.380 0.019 1.356
beta2_pelagic[9] 0.220 0.665 -1.229 0.287 1.517
beta2_pelagic[10] 0.035 0.611 -1.254 0.030 1.364
beta2_pelagic[11] 0.257 0.625 0.092 0.171 0.844
beta2_pelagic[12] 5.224 4.387 1.015 3.879 17.318
beta2_pelagic[13] 0.539 0.577 0.176 0.396 1.626
beta2_pelagic[14] 0.310 0.142 0.142 0.276 0.665
beta2_pelagic[15] 5.270 3.957 1.318 4.182 16.183
beta2_pelagic[16] 3.518 4.015 0.209 2.060 14.410
beta3_pelagic[1] 29.458 7.865 18.408 28.291 44.747
beta3_pelagic[2] 29.997 7.986 18.462 29.024 44.808
beta3_pelagic[3] 30.159 6.593 19.337 29.431 44.226
beta3_pelagic[4] 25.199 4.967 18.800 24.332 40.127
beta3_pelagic[5] 30.073 8.248 18.458 28.723 45.226
beta3_pelagic[6] 31.671 6.782 19.086 31.597 44.074
beta3_pelagic[7] 29.776 7.900 18.488 28.661 44.928
beta3_pelagic[8] 29.491 8.017 18.454 28.147 45.002
beta3_pelagic[9] 30.795 6.050 19.409 30.797 42.732
beta3_pelagic[10] 29.577 8.192 18.405 27.971 45.018
beta3_pelagic[11] 42.139 2.666 35.407 42.615 45.790
beta3_pelagic[12] 43.468 0.273 42.989 43.460 43.990
beta3_pelagic[13] 43.100 1.442 40.509 42.925 45.782
beta3_pelagic[14] 42.440 1.745 38.804 42.525 45.568
beta3_pelagic[15] 43.150 0.273 42.445 43.170 43.636
beta3_pelagic[16] 43.132 0.922 41.150 43.168 45.565
mu_beta0_pelagic[1] 0.753 1.029 -1.507 0.810 2.724
mu_beta0_pelagic[2] 1.803 0.361 1.067 1.807 2.487
mu_beta0_pelagic[3] 0.247 0.496 -0.815 0.266 1.193
tau_beta0_pelagic[1] 0.536 0.566 0.053 0.354 2.040
tau_beta0_pelagic[2] 2.827 2.840 0.295 2.050 9.991
tau_beta0_pelagic[3] 1.360 1.031 0.166 1.101 4.075
beta0_yellow[1] -0.533 0.189 -0.948 -0.525 -0.204
beta0_yellow[2] 0.493 0.190 0.074 0.504 0.798
beta0_yellow[3] -0.321 0.189 -0.701 -0.308 0.000
beta0_yellow[4] 0.809 0.277 0.086 0.851 1.187
beta0_yellow[5] -0.293 0.349 -0.985 -0.295 0.379
beta0_yellow[6] 1.117 0.164 0.798 1.114 1.438
beta0_yellow[7] 0.986 0.158 0.682 0.984 1.303
beta0_yellow[8] 1.010 0.154 0.719 1.010 1.311
beta0_yellow[9] 0.664 0.158 0.355 0.661 0.981
beta0_yellow[10] 0.593 0.144 0.318 0.590 0.873
beta0_yellow[11] -2.032 0.447 -2.913 -2.047 -1.210
beta0_yellow[12] -3.734 0.424 -4.617 -3.715 -2.955
beta0_yellow[13] -3.767 0.453 -4.804 -3.722 -2.987
beta0_yellow[14] -2.112 0.710 -3.298 -2.183 -0.247
beta0_yellow[15] -2.875 0.469 -3.883 -2.847 -2.042
beta0_yellow[16] -2.432 0.500 -3.320 -2.465 -1.415
beta1_yellow[1] 0.918 2.484 0.009 0.642 3.074
beta1_yellow[2] 1.084 0.431 0.601 1.022 2.053
beta1_yellow[3] 0.719 0.319 0.239 0.691 1.329
beta1_yellow[4] 1.407 0.754 0.637 1.188 3.756
beta1_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta1_yellow[11] 2.188 0.444 1.374 2.188 3.130
beta1_yellow[12] 2.536 0.435 1.755 2.509 3.429
beta1_yellow[13] 2.876 0.447 2.110 2.817 3.905
beta1_yellow[14] 2.215 0.665 0.601 2.262 3.421
beta1_yellow[15] 2.121 0.458 1.261 2.089 3.102
beta1_yellow[16] 2.200 0.499 1.146 2.217 3.104
beta2_yellow[1] -3.156 2.703 -9.873 -2.446 -0.058
beta2_yellow[2] -2.893 2.249 -8.961 -2.532 -0.157
beta2_yellow[3] -2.646 2.372 -9.330 -1.985 -0.134
beta2_yellow[4] -2.531 2.725 -9.348 -1.591 -0.097
beta2_yellow[5] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[6] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[7] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[8] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[9] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[10] 0.000 0.000 0.000 0.000 0.000
beta2_yellow[11] -4.936 2.956 -12.245 -4.295 -1.094
beta2_yellow[12] -5.318 2.885 -12.456 -4.724 -1.424
beta2_yellow[13] -5.162 2.812 -12.068 -4.496 -1.539
beta2_yellow[14] -5.102 3.010 -12.401 -4.580 -0.508
beta2_yellow[15] -4.639 2.875 -11.608 -3.930 -0.986
beta2_yellow[16] -5.569 2.984 -12.430 -4.963 -1.476
beta3_yellow[1] 25.876 7.134 18.259 22.868 44.305
beta3_yellow[2] 29.223 1.918 25.392 28.991 33.396
beta3_yellow[3] 32.867 3.005 25.103 32.909 38.261
beta3_yellow[4] 29.311 3.717 21.229 28.296 36.183
beta3_yellow[5] 29.972 8.082 18.415 29.022 44.975
beta3_yellow[6] 29.972 7.942 18.505 28.821 44.904
beta3_yellow[7] 30.148 7.890 18.402 29.476 44.724
beta3_yellow[8] 29.926 8.008 18.470 29.068 45.003
beta3_yellow[9] 30.066 8.018 18.442 28.966 44.860
beta3_yellow[10] 29.775 7.934 18.426 28.762 44.892
beta3_yellow[11] 45.331 0.523 44.063 45.419 45.978
beta3_yellow[12] 43.309 0.363 42.586 43.292 44.015
beta3_yellow[13] 44.894 0.378 44.042 44.959 45.548
beta3_yellow[14] 43.703 2.454 34.263 44.201 45.843
beta3_yellow[15] 45.162 0.541 44.122 45.144 45.973
beta3_yellow[16] 44.519 0.810 43.352 44.523 45.826
mu_beta0_yellow[1] 0.076 0.538 -1.080 0.078 1.144
mu_beta0_yellow[2] 0.643 0.336 -0.062 0.666 1.266
mu_beta0_yellow[3] -2.487 0.667 -3.548 -2.584 -0.864
tau_beta0_yellow[1] 1.935 2.948 0.097 1.251 7.557
tau_beta0_yellow[2] 3.501 4.165 0.317 2.321 13.780
tau_beta0_yellow[3] 1.401 1.631 0.095 0.897 5.652
beta0_black[1] -0.078 0.160 -0.389 -0.077 0.232
beta0_black[2] 1.914 0.126 1.668 1.913 2.159
beta0_black[3] 1.318 0.135 1.059 1.317 1.582
beta0_black[4] 2.430 0.135 2.171 2.433 2.694
beta0_black[5] 4.635 2.041 1.903 4.208 9.788
beta0_black[6] 4.612 1.906 2.214 4.169 9.501
beta0_black[7] 3.730 1.853 1.574 3.278 8.962
beta0_black[8] 0.955 0.209 0.550 0.952 1.377
beta0_black[9] 2.608 0.227 2.168 2.607 3.066
beta0_black[10] 1.458 0.133 1.202 1.458 1.724
beta0_black[11] 3.489 0.154 3.185 3.489 3.792
beta0_black[12] 4.868 0.172 4.525 4.873 5.196
beta0_black[13] -0.119 0.236 -0.607 -0.109 0.322
beta0_black[14] 2.859 0.159 2.548 2.857 3.163
beta0_black[15] 1.289 0.155 0.991 1.289 1.596
beta0_black[16] 4.275 0.158 3.971 4.274 4.580
beta2_black[1] 7.736 9.925 0.528 3.467 39.857
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.907 1.515 -5.642 -1.368 -0.384
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.810 1.098 39.979 41.960 43.408
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.206 0.830 37.230 39.308 40.587
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.264 0.196 -0.642 -0.263 0.117
beta4_black[2] 0.242 0.185 -0.126 0.244 0.607
beta4_black[3] -0.931 0.195 -1.311 -0.930 -0.551
beta4_black[4] 0.425 0.221 0.000 0.430 0.846
beta4_black[5] 0.533 1.285 -1.303 0.334 3.575
beta4_black[6] 0.549 1.379 -1.345 0.318 3.587
beta4_black[7] 0.454 1.170 -1.313 0.290 3.253
beta4_black[8] -0.250 0.309 -0.850 -0.244 0.355
beta4_black[9] 0.834 0.775 -0.254 0.692 2.731
beta4_black[10] 0.054 0.183 -0.306 0.056 0.414
beta4_black[11] -0.700 0.217 -1.133 -0.701 -0.283
beta4_black[12] 0.157 0.324 -0.460 0.142 0.796
beta4_black[13] -1.181 0.221 -1.613 -1.181 -0.743
beta4_black[14] -0.186 0.237 -0.632 -0.188 0.287
beta4_black[15] -0.889 0.215 -1.305 -0.895 -0.464
beta4_black[16] -0.598 0.228 -1.037 -0.599 -0.152
mu_beta0_black[1] 1.278 0.872 -0.613 1.305 3.011
mu_beta0_black[2] 2.724 1.049 0.852 2.613 5.055
mu_beta0_black[3] 2.540 0.989 0.357 2.594 4.425
tau_beta0_black[1] 0.645 0.607 0.054 0.459 2.191
tau_beta0_black[2] 0.470 0.666 0.047 0.256 2.307
tau_beta0_black[3] 0.239 0.162 0.051 0.199 0.658
beta0_dsr[11] -2.897 0.282 -3.451 -2.898 -2.334
beta0_dsr[12] 4.550 0.288 4.002 4.547 5.131
beta0_dsr[13] -1.369 0.384 -2.267 -1.334 -0.747
beta0_dsr[14] -3.666 0.522 -4.685 -3.658 -2.673
beta0_dsr[15] -1.926 0.287 -2.478 -1.920 -1.348
beta0_dsr[16] -3.002 0.369 -3.718 -3.001 -2.286
beta1_dsr[11] 4.832 0.292 4.253 4.831 5.379
beta1_dsr[12] 6.543 8.070 2.232 5.043 19.627
beta1_dsr[13] 2.910 0.530 2.257 2.848 4.402
beta1_dsr[14] 6.330 0.544 5.296 6.337 7.409
beta1_dsr[15] 3.322 0.291 2.755 3.322 3.889
beta1_dsr[16] 5.815 0.387 5.067 5.815 6.565
beta2_dsr[11] -8.281 2.393 -13.777 -8.016 -4.562
beta2_dsr[12] -6.999 2.647 -12.936 -6.849 -2.281
beta2_dsr[13] -6.417 2.988 -12.842 -6.351 -0.353
beta2_dsr[14] -6.192 2.571 -11.357 -5.995 -1.874
beta2_dsr[15] -7.765 2.447 -13.289 -7.493 -3.848
beta2_dsr[16] -7.900 2.339 -13.322 -7.628 -4.220
beta3_dsr[11] 43.486 0.150 43.212 43.482 43.770
beta3_dsr[12] 33.964 0.724 32.107 34.118 34.810
beta3_dsr[13] 43.254 0.420 42.777 43.209 43.897
beta3_dsr[14] 43.346 0.241 43.072 43.272 43.976
beta3_dsr[15] 43.508 0.188 43.165 43.504 43.857
beta3_dsr[16] 43.442 0.159 43.169 43.433 43.762
beta4_dsr[11] 0.592 0.217 0.172 0.594 1.029
beta4_dsr[12] 0.256 0.450 -0.635 0.254 1.143
beta4_dsr[13] -0.174 0.228 -0.633 -0.175 0.244
beta4_dsr[14] 0.151 0.253 -0.350 0.149 0.650
beta4_dsr[15] 0.722 0.219 0.291 0.718 1.158
beta4_dsr[16] 0.159 0.226 -0.284 0.165 0.602
beta0_slope[11] -1.843 0.146 -2.134 -1.843 -1.568
beta0_slope[12] -4.471 0.254 -4.983 -4.464 -3.994
beta0_slope[13] -1.356 0.196 -1.839 -1.341 -1.021
beta0_slope[14] -2.675 0.165 -2.994 -2.675 -2.349
beta0_slope[15] -1.344 0.147 -1.626 -1.344 -1.055
beta0_slope[16] -2.739 0.156 -3.042 -2.738 -2.427
beta1_slope[11] 4.491 0.223 4.060 4.491 4.932
beta1_slope[12] 3.991 0.449 3.140 4.002 4.881
beta1_slope[13] 2.746 0.494 2.210 2.649 4.378
beta1_slope[14] 6.319 0.420 5.555 6.307 7.193
beta1_slope[15] 3.013 0.212 2.596 3.013 3.430
beta1_slope[16] 5.285 0.286 4.724 5.292 5.841
beta2_slope[11] 8.621 2.264 5.195 8.269 13.921
beta2_slope[12] 6.653 2.857 1.185 6.609 12.612
beta2_slope[13] 5.276 2.997 0.338 5.318 10.978
beta2_slope[14] 6.320 2.458 2.279 6.169 11.867
beta2_slope[15] 8.208 2.361 4.543 7.925 13.672
beta2_slope[16] 7.761 2.204 4.238 7.508 12.739
beta3_slope[11] 43.460 0.134 43.216 43.455 43.720
beta3_slope[12] 43.356 0.269 42.905 43.317 43.894
beta3_slope[13] 43.475 0.414 42.891 43.428 44.172
beta3_slope[14] 43.269 0.135 43.095 43.237 43.626
beta3_slope[15] 43.494 0.162 43.196 43.496 43.797
beta3_slope[16] 43.366 0.140 43.150 43.345 43.681
beta4_slope[11] -0.734 0.163 -1.061 -0.729 -0.424
beta4_slope[12] -1.172 0.475 -2.160 -1.131 -0.344
beta4_slope[13] 0.089 0.163 -0.224 0.090 0.414
beta4_slope[14] -0.095 0.200 -0.486 -0.097 0.297
beta4_slope[15] -0.766 0.158 -1.081 -0.765 -0.452
beta4_slope[16] -0.162 0.176 -0.506 -0.163 0.183
sigma_H[1] 0.197 0.054 0.100 0.195 0.309
sigma_H[2] 0.171 0.030 0.120 0.169 0.235
sigma_H[3] 0.197 0.042 0.122 0.193 0.287
sigma_H[4] 0.418 0.077 0.296 0.410 0.596
sigma_H[5] 0.993 0.211 0.608 0.986 1.436
sigma_H[6] 0.421 0.199 0.042 0.418 0.824
sigma_H[7] 0.310 0.067 0.209 0.300 0.470
sigma_H[8] 0.417 0.094 0.272 0.406 0.612
sigma_H[9] 0.526 0.128 0.328 0.509 0.820
sigma_H[10] 0.212 0.042 0.138 0.209 0.307
sigma_H[11] 0.277 0.046 0.201 0.273 0.375
sigma_H[12] 0.433 0.169 0.202 0.406 0.790
sigma_H[13] 0.220 0.039 0.155 0.217 0.305
sigma_H[14] 0.508 0.094 0.345 0.502 0.716
sigma_H[15] 0.247 0.040 0.178 0.243 0.336
sigma_H[16] 0.226 0.043 0.155 0.221 0.322
lambda_H[1] 2.985 3.613 0.146 1.721 12.663
lambda_H[2] 8.037 7.775 0.795 5.902 28.276
lambda_H[3] 6.298 10.502 0.308 3.176 30.039
lambda_H[4] 0.006 0.004 0.001 0.005 0.018
lambda_H[5] 3.538 7.321 0.036 1.021 26.562
lambda_H[6] 7.540 15.096 0.008 0.996 49.721
lambda_H[7] 0.013 0.009 0.002 0.011 0.034
lambda_H[8] 8.044 10.568 0.060 4.421 36.874
lambda_H[9] 0.016 0.010 0.003 0.013 0.041
lambda_H[10] 0.313 0.886 0.034 0.196 1.079
lambda_H[11] 0.298 0.997 0.012 0.133 1.318
lambda_H[12] 5.007 6.831 0.170 2.849 22.547
lambda_H[13] 3.570 3.171 0.247 2.693 11.747
lambda_H[14] 3.465 4.433 0.199 2.025 16.036
lambda_H[15] 0.026 0.050 0.003 0.016 0.099
lambda_H[16] 0.915 1.413 0.047 0.472 4.653
mu_lambda_H[1] 4.308 1.864 1.263 4.093 8.414
mu_lambda_H[2] 3.865 1.964 0.546 3.673 7.899
mu_lambda_H[3] 3.527 1.842 0.782 3.227 7.742
sigma_lambda_H[1] 8.650 4.323 2.263 7.983 18.256
sigma_lambda_H[2] 8.391 4.632 0.935 7.748 18.132
sigma_lambda_H[3] 6.247 3.902 1.079 5.454 15.968
beta_H[1,1] 6.913 1.066 4.390 7.077 8.560
beta_H[2,1] 9.883 0.486 8.895 9.902 10.784
beta_H[3,1] 8.016 0.767 6.199 8.114 9.245
beta_H[4,1] 9.339 7.726 -6.767 9.757 24.163
beta_H[5,1] 0.108 2.362 -4.910 0.306 4.207
beta_H[6,1] 3.043 3.957 -6.920 4.555 7.553
beta_H[7,1] 0.480 5.771 -12.113 0.926 10.625
beta_H[8,1] 1.686 5.576 -2.507 1.277 3.762
beta_H[9,1] 13.198 5.663 1.904 13.147 24.555
beta_H[10,1] 7.033 1.699 3.408 7.114 10.297
beta_H[11,1] 5.154 3.480 -2.653 5.901 10.004
beta_H[12,1] 2.585 1.023 0.739 2.549 4.782
beta_H[13,1] 9.021 0.911 7.091 9.088 10.454
beta_H[14,1] 2.164 1.043 0.114 2.155 4.295
beta_H[15,1] -6.189 3.854 -13.011 -6.467 2.351
beta_H[16,1] 3.361 2.549 -0.749 3.040 9.635
beta_H[1,2] 7.900 0.246 7.398 7.903 8.359
beta_H[2,2] 10.026 0.137 9.747 10.030 10.299
beta_H[3,2] 8.943 0.201 8.537 8.950 9.355
beta_H[4,2] 3.567 1.481 0.769 3.494 6.643
beta_H[5,2] 1.975 0.927 0.092 2.004 3.716
beta_H[6,2] 5.706 1.030 3.308 5.865 7.273
beta_H[7,2] 2.655 1.083 0.710 2.605 4.931
beta_H[8,2] 2.912 1.436 0.975 3.148 4.211
beta_H[9,2] 3.459 1.100 1.381 3.417 5.734
beta_H[10,2] 8.208 0.354 7.466 8.220 8.868
beta_H[11,2] 9.755 0.631 8.811 9.635 11.138
beta_H[12,2] 3.951 0.379 3.247 3.933 4.748
beta_H[13,2] 9.105 0.253 8.637 9.098 9.616
beta_H[14,2] 4.024 0.354 3.339 4.021 4.758
beta_H[15,2] 11.370 0.697 9.881 11.405 12.673
beta_H[16,2] 4.528 0.789 3.042 4.525 6.105
beta_H[1,3] 8.463 0.244 8.043 8.448 8.966
beta_H[2,3] 10.063 0.116 9.825 10.066 10.287
beta_H[3,3] 9.612 0.160 9.304 9.609 9.941
beta_H[4,3] -2.488 0.889 -4.212 -2.473 -0.782
beta_H[5,3] 3.858 0.612 2.612 3.879 5.033
beta_H[6,3] 7.946 1.189 6.342 7.553 10.528
beta_H[7,3] -2.775 0.666 -4.113 -2.768 -1.468
beta_H[8,3] 5.298 0.659 4.653 5.196 6.507
beta_H[9,3] -2.807 0.736 -4.246 -2.816 -1.352
beta_H[10,3] 8.687 0.277 8.149 8.677 9.266
beta_H[11,3] 8.559 0.289 7.929 8.590 9.054
beta_H[12,3] 5.259 0.321 4.478 5.305 5.779
beta_H[13,3] 8.843 0.176 8.495 8.846 9.179
beta_H[14,3] 5.726 0.279 5.102 5.743 6.230
beta_H[15,3] 10.364 0.319 9.747 10.356 11.006
beta_H[16,3] 6.312 0.580 5.069 6.355 7.347
beta_H[1,4] 8.259 0.177 7.879 8.269 8.572
beta_H[2,4] 10.126 0.119 9.869 10.134 10.330
beta_H[3,4] 10.107 0.168 9.736 10.122 10.394
beta_H[4,4] 11.798 0.461 10.884 11.794 12.691
beta_H[5,4] 5.528 0.751 4.299 5.440 7.285
beta_H[6,4] 7.003 0.932 4.959 7.295 8.255
beta_H[7,4] 8.292 0.357 7.561 8.300 8.966
beta_H[8,4] 6.695 0.295 6.170 6.716 7.135
beta_H[9,4] 7.192 0.462 6.334 7.185 8.113
beta_H[10,4] 7.731 0.233 7.292 7.727 8.208
beta_H[11,4] 9.390 0.203 8.983 9.392 9.797
beta_H[12,4] 7.149 0.208 6.756 7.146 7.591
beta_H[13,4] 9.040 0.140 8.757 9.042 9.308
beta_H[14,4] 7.739 0.220 7.311 7.739 8.182
beta_H[15,4] 9.468 0.234 9.014 9.469 9.922
beta_H[16,4] 9.346 0.229 8.926 9.339 9.814
beta_H[1,5] 8.982 0.145 8.683 8.986 9.257
beta_H[2,5] 10.778 0.095 10.592 10.778 10.972
beta_H[3,5] 10.909 0.171 10.606 10.899 11.263
beta_H[4,5] 8.381 0.476 7.471 8.369 9.327
beta_H[5,5] 5.428 0.592 3.989 5.473 6.460
beta_H[6,5] 8.828 0.638 7.906 8.666 10.326
beta_H[7,5] 6.746 0.350 6.076 6.743 7.459
beta_H[8,5] 8.224 0.248 7.858 8.200 8.705
beta_H[9,5] 8.207 0.479 7.228 8.214 9.168
beta_H[10,5] 10.096 0.228 9.658 10.096 10.554
beta_H[11,5] 11.503 0.231 11.060 11.504 11.953
beta_H[12,5] 8.486 0.199 8.087 8.491 8.883
beta_H[13,5] 9.995 0.137 9.719 9.993 10.260
beta_H[14,5] 9.200 0.233 8.774 9.193 9.693
beta_H[15,5] 11.159 0.245 10.677 11.159 11.627
beta_H[16,5] 9.934 0.170 9.580 9.939 10.248
beta_H[1,6] 10.182 0.191 9.848 10.160 10.596
beta_H[2,6] 11.517 0.112 11.300 11.516 11.741
beta_H[3,6] 10.817 0.160 10.468 10.823 11.109
beta_H[4,6] 12.900 0.840 11.235 12.921 14.479
beta_H[5,6] 5.913 0.615 4.824 5.891 7.106
beta_H[6,6] 8.799 0.691 6.956 8.938 9.779
beta_H[7,6] 9.886 0.597 8.710 9.883 11.064
beta_H[8,6] 9.496 0.339 8.894 9.528 9.963
beta_H[9,6] 8.476 0.781 7.003 8.457 10.047
beta_H[10,6] 9.508 0.321 8.811 9.536 10.047
beta_H[11,6] 10.821 0.350 10.085 10.838 11.457
beta_H[12,6] 9.382 0.260 8.879 9.375 9.928
beta_H[13,6] 11.043 0.164 10.745 11.037 11.371
beta_H[14,6] 9.831 0.301 9.243 9.834 10.402
beta_H[15,6] 10.845 0.433 9.976 10.852 11.716
beta_H[16,6] 10.539 0.229 10.038 10.549 10.958
beta_H[1,7] 10.823 0.891 8.710 10.941 12.267
beta_H[2,7] 12.213 0.449 11.251 12.230 13.037
beta_H[3,7] 10.563 0.649 9.173 10.615 11.676
beta_H[4,7] 2.363 4.280 -5.593 2.273 11.062
beta_H[5,7] 6.400 1.776 3.127 6.388 10.110
beta_H[6,7] 9.708 2.483 4.742 9.638 16.024
beta_H[7,7] 10.430 2.989 4.412 10.402 16.386
beta_H[8,7] 11.026 1.356 9.339 10.919 13.352
beta_H[9,7] 4.434 4.037 -3.715 4.464 12.293
beta_H[10,7] 9.855 1.445 7.303 9.750 12.981
beta_H[11,7] 10.949 1.690 7.768 10.823 14.609
beta_H[12,7] 9.990 0.989 7.840 10.069 11.624
beta_H[13,7] 11.674 0.745 10.023 11.755 12.837
beta_H[14,7] 10.411 0.966 8.340 10.447 12.189
beta_H[15,7] 11.951 2.293 7.408 11.936 16.468
beta_H[16,7] 12.281 1.246 10.237 12.117 15.178
beta0_H[1] 8.935 12.933 -17.009 9.004 35.207
beta0_H[2] 10.719 6.430 -2.092 10.681 23.447
beta0_H[3] 10.011 9.607 -8.743 9.861 29.730
beta0_H[4] 8.504 193.272 -394.052 13.410 399.750
beta0_H[5] 5.025 24.287 -41.769 4.528 53.957
beta0_H[6] 8.090 49.441 -100.792 7.622 121.089
beta0_H[7] 5.861 136.033 -277.143 7.065 268.145
beta0_H[8] 7.080 44.348 -17.858 6.490 32.525
beta0_H[9] 6.779 116.164 -218.850 5.694 249.858
beta0_H[10] 8.045 32.643 -58.450 8.408 74.419
beta0_H[11] 8.235 47.944 -105.381 9.614 105.122
beta0_H[12] 6.664 12.451 -15.647 6.630 30.334
beta0_H[13] 9.750 11.230 -9.351 9.778 31.122
beta0_H[14] 6.620 12.085 -16.852 6.640 31.788
beta0_H[15] 8.068 108.015 -215.649 8.096 233.368
beta0_H[16] 8.769 24.204 -38.987 8.421 59.683